The Elucidation of Terraced Housing in Iranian Vernacular Architecture through Fractal Models: In Case of Masouleh and Abyaneh Settlements

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The Elucidation of Terraced Housing in Iranian

Vernacular Architecture through Fractal Models: In

Case of Masouleh and Abyaneh Settlements

Ehsan Reza

Submitted to the

Institute of Graduate Studies and Research

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in

Architecture

Eastern Mediterranean University

July 2016

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Approval of the Institute of Graduate Studies and Research

Prof. Dr. Cem Tanova Acting Director

I certify that this thesis satisfies the requirements as a thesis for the degree of Doctor of Philosophy in Architecture.

Prof. Dr. Özgür Dinçyürek Chair, Department of Architecture

We certify that we have read this thesis and that in our opinion it is fully adequate in scope and quality as a thesis for the degree of Doctor of Philosophy in Architecture.

Prof. Dr. Özgür Dinçyürek Supervisor Examining Committee 1. Prof. Dr. Özgür Dinçyürek

2. Prof. Dr. Kokan Grchev

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ABSTRACT

The Latin term “Vernaculus” which means ‘native’ generates the terminology of vernacular architecture. It represents the architecture of people that defining the built environment. Accordingly, this terminology makes reference to the sense of place attachments to the designated context by the inhabitants, wherein they are rooted in the specific origin points that refer to their distinct race and homeland.

This research is based on identifying the vernacular architecture of Iran; specifically by focusing on steepy land context so-called terraced housing. Aimed to drive fruitful design principles qualified to be applicable to contemporary architecture, are investigated. It should be noticed that Iranian terraced housing precedence have been remained literally unique in accordance with their local entity and heterogeneity among their topography; in comparison with various form of terraced housing all around the world.

The identification of these settlements was evaluated according to the topography, climate, urban pattern and spatial organization of Iranian terraced settlements. As an outcome, the analysis of case studies and data processing will enable decision makers, planners, architects and designers to become more aware of the existing architectural ritual. The contemporary housing design problems can be solved by employing an appropriate method of design and building construction with reference to the present vernacular housing stock.

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geometry that is based on mathematical algorithm. Fractal geometry is particularly focusing on organic patterns, which have been developed and diversified in vernacular architecture. There are many useful thoughts that can be learnt from the organic patterns and from searching for the randomness and self-similarity of a vernacular settlement.

This study is going to investigate some critical points of the application of box-counting method to the evaluation of fractal dimension of some chosen vernacular settlements. The relationships amongst the topography, elevation and urban pattern are analyzed in two selected Iranian terraced settlements; Masouleh and Abyaneh.

The investigation will be accomplished through fractal analysis of two different villages in different geography of Iran. By referring to the fractal dimension calculated with box-counting method, different type of information will be collected about mentioned vernacular settlements. The new housing pattern will be proposed according to the cellular automata theory.

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ÖZ

Yöresel mimarlık, Latince ‘vernaculus’ kelimesinden türeyip, ‘yerli’ anlamındadır. Yapı çevresini tanımlaya yerel insanların mimarisini temsil etmektedir. Bu terminoloji, insanların bölgeye olan aidiyeti, nereden oldukları, kendi orijinal ırkı veya memleketinin temsili anlamına gelir.

Teras evleri (basamak/merdiven konut) adı ile bilinen, İran’da eğimli arazide gelişen yöresel mimarinin, yararlı tasarım prensiplerini analiz ederek çağdaş mimariye uygulamak, bu çalışmanın temelini oluşturmaktadır. Tüm dünyada birçok örneği bulunmakla birlikte, İran teras evleri bu coğrafyadaki yöresel zenginliği ve farklılıkları ile eşsizdir. Bu köylerin belirlenmesi İran teraslı yerleşkelerinin, iklim, kentsel doku ve mekansal organizasyonuna göre değerlendirilmiştir. Sonuç olarak, örnek çalışmalar ve oluşturulacak veri tabanı sayesinde planlamacılar, mimarlar ve tasarımcılar, mevcut mimari doku hakkinda daha çok bilgi sahibi olacaklardır. Çağdaş konut tasarım sorunları; uygun tasarım yöntemleri ve yapım teknikleri kullanılarak ve mevcut geleneksel konut stokunu referans alarak çözülebilir.

Yirminci yüzyılın ikinci yarısında, geleneksel yerleşim oluşumunu ve gelişimini incelemek amacıyla birçok farklı yöntemler kullanılmıştır. Bunlardan birisi matematiksel algoritmaya dayanan fraktal geometridir. Fraktal geometride, özellikle gelişmiş ve yöresel mimaride çeşitlenmiş organik desenler üzerinde durulmaktadır.

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Bu çalışma, bazı seçilmiş yerel yerleşim birimlerinin fraktal boyutunun değerlendirilmesi ve kutu sayma yönteminin uygulanmasındaki bazı kritik noktaları araştırmaktadır. Topografya, görünüş/cephe ve kent dokusu arasındaki ilişkilerden dolayı seçilen iki İran teraslı yerleşim yeri, Masouleh ve Abyaneh, analiz edilmektedir

Araştırma, İran’ın iki farklı coğrafi bölgesinde bulunan köylerin fraktal analizi yoluyla gerçekleştirilecektir. Kutu - sayma yöntemi ile hesaplanan fraktal boyuta atıfta bulunarak, ilgili yöresel yerleşim yerleri hakkında farklı bilgi türleri elde edilecektir. Hücresel otomata teorisine göre yeni konut örüntüsü önerilecektir.

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ACKNOWLEDGMENT

First of all, I would like to fully extend my respect to my invaluable supervisor, Prof. Dr. Özgür Dinçyürek; and my gratitude for his academic guidance, which always encouraged me more in the process of completing this study. There is no doubt that without his precise supervisions and constructive comments this research would not have been successfully done.

I would like also to appreciate the members of scientific committee, Assoc. Prof. Dr. Asu Tozan and Assoc. Prof. Dr. Özlem Olgaç Türker; who have deliberatively contributed all the time to the progress, and the process of assessment for this dissertation.

I would like to express all my appreciation to Prof. Dr. Prof. Dr. Yonca Hürol for all her academic efforts aiming to provide a ground for doing such a study.

Moreover, it should be stated that the study would not have been possible without kindnesses and also precious motivations given by Assoc. Prof. Dr. Sadiye Müjdem Vural, and my friend Kamiar Yazdani. Also, I would like to extend my appreciation to Assist. Prof. Dr. Öznem Şahali for her valuable support in this process.

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LIST OF TABLES

Table 1: The comparison of Euclidean geometry with fractal geometry ... 47

Table 2: The description of fractal dimension methods ... 50

Table 3: Box counting For the Robie House elevation ... 52

Table 4: Box-counting grids placed over elevations of the Robie House ... 53

Table 5: The fractal dimension of Amasya, Turkey ... 85

Table 6: The box-counting of Masouleh and Abyaneh’ s elevation ... 93

Table 7: The box-counting of Masouleh and Abyaneh Urban Patterns ... 99

Table 8: Comparison of Fractal Dimenssions calculated for Amasya ... 101

Table 9: Masouleh village Environmental Fractal Analysis ... 102

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LIST OF FIGURES

Figure 1:Effective Factors in Shaping Villages ... 18

Figure 2: Map of Iran with the Location of Villages Kandovan, Masouleh, Abyaneh, Maymand ... 23

Figure 3: Map of Iran, Location of Masouleh and Abyaneh ... 24

Figure 4: Section and Angle of Masouleh Village and Abyaneh Village ... 25

Figure 5: Climatic Map of Iran ... 26

Figure 6: Climatic Map of Iran and Building Typologies ... 28

Figure 7: Location of Masouleh and Abyaneh Villages ... 31

Figure 8: Location of Masouleh and Abyaneh on the Border of Different Climatic Regions ... 32

Figure 9: Situation Map, Combination of Private and Public Spaces and the Urban Fabric of Masouleh and Abyaneh………...34

Figure 10: Four Jumps to Consciousness ... 36

Figure 11: Symmetry Break Terrace, Scotland ... 36

Figure 12: The Formation of the Sierpinski Gasket ... 41

Figure 13: Introducing Randomness ... 42

Figure 14: The Counted Boxes from the Box-Counting Analysis of the Robie House Elevation ... 54

Figure 15: A photograph of a Forest, an artistic rendition of a landscape and painted lines ... 56

Figure 16: Fractal Lines of Increasing Dimension ... 58

Figure 17: A Photograph of a Forest and an artistic rendition of a landscape ... 59

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Figure 19: Kendariya Mahadeo Temple ... 61

Figure 20: The Rising, Fractal-like Shikharas of Kandariya Temple in Khajuraho. Stella Kramrisch's book, The Hindu Temple ... 62

Figure 21: Basic Cellular Automata Terminology ... 68

Figure 22: Three-dimensional Cellular Automata ... 68

Figure 23: Sample Generation ... 70

Figure 24: Transition Rules of the Game of Life ... 71

Figure 25: First Iteration of Masouleh Elevation ... 87

Figure 26: First Iteration of Abyaneh Elevation ... 87

Figure 27: Box-counting; First iteration of Masouleh elevation ... 88

Figure 28: Box-counting; First iteration of Abyaneh elevation ... 88

Figure 29: Box-counting; Second Iteration of Masouleh elevation ... 89

Figure 30: Second iteration of Masouleh and Abyaneh elevation ... 89

Figure 31:Box-counting; Third iteration of Masouleh elevation ... 90

Figure 32: Box-counting; Third iteration of Abyaneh elevation ... 90

Figure 33: Box-counting; Fourth iteration of Masouleh elevation ... 91

Figure 34: Box-counting; Fourth iteration of Abyaneh elevation ... 91

Figure 35: Box-counting; Fifth Iteration of Masouleh elevation ... 92

Figure 36: Box-counting; Fifth Iteration of Abyaneh elevation ... 92

Figure 37: Box-counting; First Iteration of Masouleh urban pattern ... 94

Figure 38: Box-counting; First Iteration of Abyaneh urban pattern ... 94

Figure 39: Box-counting; Second Iteration of Masouleh urban pattern ... 95

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Figure 43: Box-counting; Fourth Iteration of Masouleh urban pattern ... 97

Figure 44: Box-counting; Fourth Iteration of Abyaneh urban pattern ... 97

Figure 45: Box-counting; Fifth Iteration of Masouleh urban pattern ... 98

Figure 46: Box-counting; Fifth Iteration of Abyaneh urban pattern ... 98

Figure 47: Generation of Matrix [128, 32] ... 105

Figure 48: Generation of Matrix 2 ... 105

Figure 49: Masouleh Iteration 0 , Cellular Automata ... 105

Figure 55: Abyaneh Iteration 0 , Cellular Automata ... 107

Figure 61: Combination of Iterations, Masouleh , Cellular Automata ... 108

Figure 62: Combination of Iterations, Abyaneh , Cellular Automata ... 108

Figure 63: Masouleh, Isometric View Simulation of CA Results ... 109

Figure 64: Masouleh, Urban Pattern’s Simulation of CA Results ... 109

Figure 65: Masouleh, Elevation’s Simulation of CA Results ... 109

Figure 66: Abyaneh, Isometric View Simulation of CA Results ... 110

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Chapter 1 INTRODUCTION

1.1 Problem Statement

Architecture and human needs are in direct relation in first step. Indeed, interfacing of mentioned concepts are always impacted by several parameters including; culture, economy, politics, society, religion and beliefs, which generate local identity together with formal approaches in built settings as the result.

Disregarding the know-how and mislaid of local identity from prior descendant in architectural discipline, began to emerge in the period of the industrial revolution and vested afterwards. A thoughtful problem in identity and arrangement of the built environment has been caused by detachments of human beings from nature and ignorance to the admiration of the existing environmental settlements.

As a result, the contemporary decision makers and emerged a kind of “identity crisis” in architecture, are evident of disappearance of some major factors including contextual design, environment friendly concerns in building design and regards to the cultural patterns.

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very complicated. Formal architectural approaches have used mostly Euclidean geometry that represents pure volumes that can be defined by regular forms. Organic geometries do not have certain shape and organization like natural objects such as mountains.

Vernacular architecture has this organic geometry of natural objects whereas contemporary settlements are mostly forming a totally different geometry than the natural environment. In this context, in the light of vernacular architecture, nature friendly design approaches, which are generally lost in contemporary cities, can be achieved. By understanding the necessities of vernacular architecture, it is highly important to revive the traditional techniques in today’s architecture. There is a vital need to think about and examine a few areas as contextual investigations; find their possibilities, put the consequence of studies all together, exhibit them by order, and finally as a result, introducing them as applicable model in contemporary architecture.

1.2 Aim and Objective

In the dissertation, it is aimed to prove the necessity of the systematic development of the vernacular architecture by proposing new methodology for the further studies of new housing developments in contemporary architecture.

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main tool, therefore, understanding the importance of the usage of it, in contemporary design and architecture will be explained. Moreover, it should be mentioned that fractal geometry is based on the density ratio of pattern. Therefore by focusing on the term pattern, the fractal geometry and fractal dimension will be explained.

According to this ideology the general description of fractal theory and geometry will be clarified from many different points of view of scholars; therefore, simulation of these villages will be done by the help of analysis of some specific villages, in contemporary architecture.

1.3 Research Limitation

This study will be the result of four different professions; physics, mathematics, computer software and architecture. By considering the multi-dimensional essence of this research, the limitation should be appropriately characterized to accomplish the accurate result. In this sense, topographical constrain, significantly generates the initial limitation of the research. Amid this study, only the urban vernacular settlements, which are placed on steep topography, will be sought. Terraced houses are an architectural solution for steep topography. Without any doubt, Iran is a country surrounded by various mountains. Accordingly, by considering the existence of the variations in topography, geographical and climatic issues related, hence there are many thoughtful lessons that can be learnt in the light of vernacular architecture of the region. Moreover, the dense housing in urban vernacular settlements can be enlightening the contemporary dense housing.

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have certain patterns. With the help of fractal geometry, mentioned patterns within the local building culture would be found. For finding the fractal geometry and regenerating the pattern, fractal dimension has to be calculated. There are many different methods for finding fractal dimension such as walking-divider, box counting, prism counting, epsilon-blanket, perimeter-area relationship, hybrid, power spectrum, fractional Brownian motion, variogram, isarithm, etc. in many different fields. By comparing different mentioned methodology, it could be concluded that, box-counting method, in architecture, is the most reliable and practical methodology. For this reason, box-counting method will be used for finding the fractal dimension in this study. Also there are many software and programmes, which are available for simulation of those rural settlements, but Fractal Analysis System for Windows, fractal3 by Hiroyuki Sasaki is the programme (based on box counting algorithm) that will be used in this study. Finally cellular automata methodology will be used for proposing new settlements.

1.4 Research Methodology

According to the diverse interpretation of researchers from different disciplines in term of architects, mathematicians, urban planners, decision makers, computer software developers, etc., numerous approaches can be followed in the following studies.

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architecture, contemporary housing, settlement pattern, fractal geometry, fractal dimension and investigating the references relative with formal and functional approaches to the vernacular architecture.

• Data collection: To investigate collected data of housing based on vernacular architecture literature, it will be fruitful to declare a domestic investigation in its distinctive vernacular architecture. This will be applied by getting aid of: o Photography Documentations

o Sketches of cases on the site

o Data analysis of the plans and elevations.

o Finding the proportions and ratios of these organic settlements according to the fractal geometries, by box counting (graphical and mathematical). o Collecting data, analysing and decoding them manually according to

fractal geometries (finding fractal dimensions) and computerizing them by “fractal3” software for reviving the vernacular architecture in contemporary architecture.

o Cellular automata (CA) for the concept of growth will be used to form new housing proposals.

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The study continues by deep description of fractal theories, and definition of fractal dimension is given. As it is very wide topic and it is not just summarized in architectural borders so clarification of this subject is one of the most initial study in this investigation. Also the hypothesis of the study and the method used are explained in detail and applied on the case studies.

Simulation of the process is done by “Cellular automata” computational method which can simulate the contemporary housing proposal due to the simple rules of growth which are based on Conway’s game of life theory.

Parallel to the mentioned descriptions, hypothesis was tested on the mentioned case studies. Masouleh and Abyaneh settlements are examined via urban pattern, elevation and environmental organization and the fractal dimension of both villages were going to calculate.

Finally, a methodology is developed to propose a new housing in metropolitan cities. The result of this proposal is the intersection or junction of the vernacular architecture and contemporary architecture, which can prove the meaning of sustainability in many different dimensions.

1.5 Background of the Study

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More currently, on one hand, Iranian rural settlements have been affected by internal migration of inhabitants to the urban contexts. On the other hand, with regard to challenging condition of living, which is rooted in the degree of excellence of building techniques and expensive maintain coasts, the inhabitants have been uprooted to transfer from their own vernacular origin points to the cities.

Besides, the existing problems of urban settlements can be sought through outstanding features of vernacular architecture (Oliver, 1997). Consequently, data collection of mentioned principles, are worthy to be discovered in order to utilize in architectural discipline.

Hence, basing on two varied zones of Iran, the research is aimed to inspect the local terraced dwellings in those specific zones. In general, it is intended to introduce the vernacular architecture and more importantly, to extract applicable principles toward the problems of current housing developments.

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Chapter 2 GENERAL OVERVIEW ON VERNACULAR

SETTLEMENTS

2.1 The General Characteristics of Vernacular Architecture

“Vernacular Architecture as derived from the Latin word “Vernaculus” means native”, which has good reason to be recalled as “the architecture of the people” (Oliver, 1997, p. xxi).

The word “Vernacular” have a broad definition, which becomes a significant notion, by interfacing of various parameters such as; indigenous, folk, primitive, widespread, and spontaneous.

Moreover, Rudofsky defined vernacular architecture as: “Architecture without architect and non-pedigreed architecture”(Rudofsky, 1964, p. 1).

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environment is formed to rectify the needs and the lifestyle of inhabitants (Reza, 2011).

In addition, Oliver (2003), in his book named ‘Dwellings’, determines that: “It is contended that popular architecture designed by professional architects or commercial builders for popular use, does not come within the compass of the vernacular.” Likewise, Oliver proposes the simple definition of vernacular architecture as “the architecture of the people, and by the people, but not for the people” (Oliver, 2003).

According to that, as Dincyurek quote from Sancar (1991); “Vernacular is the architecture of the common, ordinary people not upper class or avant-garde, and cuts across all scales with repeated patterns or ideal types with variations, which can be found at the artifact, building and settlement scale” (Dincyurek, 2002, p. 16).

As Oktay (2006), remarked in her unpublished master thesis (2006), “Definition of ‘vernacular architecture’ covers cultural attributes, environmental factors and economic circumstances. In this manner, climate topography/site, available resource, existing technology, time, locality, culture, way of life can be classified as the predominantly used key words while explaining the term” (Oktay, 2006).

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with thought and feeling rather than in base or strictly utilitarian manner” (Lawrence, 1987, pp. 16-17).

Correspondingly, the building techniques of vernacular architecture are learned through experiences and by master-apprentice relationship throughout the history. There is no main manuscript defining the specific style, distinct calculation and drawings for building techniques of vernacular architecture. Moreover, builders are the subjects in these regions, who have adequate knowledge about environmental factors, cultural context, lifestyle and needs of inhabitants. In other concept, vernacular buildings are accomplished as the substantive response to the daily-based needs of the inhabitants (Reza, 2011).

For clarification of the term, “vernacular architecture” there is a compulsory need to define the place of vernacular architecture in the built environment and then the identification of vernacular architecture should deeply analyze.

Classification of vernacular of built environment can be done in various ordering. Though, Rapoport recommended a threefold division of the built environments. (Rapoport, 1969).

• Primitive- Very few building types, a model with few individual variations, built by all. (Tribal Culture).

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• High styles or grand design- (Of which modern architecture is a special case) – Many signified building typologies in which buildings is an authentic entity (however it may be changing), designed and constructed by groups of professionals.

As a consequence, vernacular terminology addresses to belonging of inhabitants to the specific regions whereby, they are grown up and the places, which represent their origin points. In such a case, the concepts of identity, scene of belonging and the heritages correlate with the words nationality and hometown (Reza, 2011, p. 10).

As the result, investigation of vernacular architecture was done by various research methodologies. In addition, in the process of asserting this kind of categorization, might introduce a degree of limitation that permit scholars to concentrate on their own research aims more precisely.

Instead, Oliver categorizes the vernacular architecture as; Aesthetic, anthropological, archaeological, architectural, behavioural, cognitive, conservationist, developmental, diffusionist, ecological, ethnological, evolutionary, folkloristic, geographical, historical, museological, phenomenological, recording and documentation, spatial, structuralist, and generative-transformational (Oliver, 1997; Reza, 2011, p. 14).

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into the physical form of culture, its needs and value – as well as the creative, desires, dreams, and passions of a people” (Cavalcanti, 1996).

To be able to understand the issue of tradition precisely, the actual concept of tradition requires some evaluation. In this respect, it has been argued amongst many scholars in the fields of anthropology, geography, history and archaeology and taken into consideration in vernacular architecture. The concept of tradition, in respect of the view of vernacular architectural knowledge, can be described as the representation of a dynamic past for contemporary people to interpret, integrate transmit and adapt to present and future building construction (Vellinga & Asquith, 2006; Heath, 2009).

To get benefit of traditional method in architecture today, there is an vitality to investigate and focus on particular districts, in order to discover their potential, to then organize the results of these studies and to present them in a categorized way, with a view to, subsequently, putting them forward as principles to be applied in the future proposals of new settlements (Reza, 2011).

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Nazar Alsayad commented on the study of regional architecture as follows: “Traditions are also ever changing but they somehow do not die easily. However, I have argued elsewhere that the built environments of the new global order exhibit a sense of placelessness resulting possibly from the fact that tradition and the practices of the vernacular are increasingly becoming less place rooted and more informational based” (Heath, 2009).

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2.2 Global Approaches that Shaping the Pattern of Vernacular

Architecture of the World (Organic Architecture)

Vernacular Architecture has multi diverse classification due to the aim of different disciplines such as nonprofessional (informal) and professional architects (formal), Sociologists, Anthropologists, Geographers, Psychologists, Geologist and others.

According to mention fields, there are various approaches and terminologies due to their demands, which in some the possibilities of sharing criteria’s are high.

Different scholars proposed many different categorizations and classifications of mentioned approaches. This dissertation mainly focused on Lawrence’s study (1987), which was one of the pioneers. It should be mentioned that following terminology still is using in recent researches. Ozgur Dincyurek used same methodology in his dissertation in 2002.

• The aesthetic/formalist interpretation; • The typological approach;

• Evolutionary theory;

• Diffusionism: social and geographical;

• Physical explanations: building technology, material, site and climate; • Social explanation: defense, economy, and household structure;

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As it was mentioned the interpretation has been categorized into seven different disciplines. On the other hand, classification of “Encyclopedia of Vernacular Architecture of the World’s Classifications” was defined in subsequent section.

• Aesthetic • Anthropological • Archaeological • Architectural • Behavioral • Cognitive • Conservationist • Developmental • Diffusions • Ecological • Ethnographical • Evolutionary • Folkloristic • Geographical • Historical • Museological • Phenomenological

• Recording and Documentation • Spatial

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It should be mentioned that, interpretation of all given approaches need deep discussion, which is not in the aim this dissertation. Therefore, some of terminologies, which are going to be examined, will be justify.

As Oliver, describe the “architectural studies terminology” as a tool to uncover the technological and organizational principles and bring defined methodologies of analysis to vernacular buildings (Oliver, 1997, pp. 1-2).

Architectural studies on vernacular architecture in terms of the sharing of knowledge, "know-how," or "technology" was transferred in between different generations.

Also as Pavlides, claimed; diversity and quantity of architectural practice due to the manifest of vernacular architecture were increased in past decade. Distinctive interpretation of architecture extract from mention statements which called as; iconic architecture, picturesque evocation of symbolic identity; architecture as determined by climate, material or function; and architecture as embodiment of experiential, emotional, spiritual and sensory qualities (Pavlides, 1997, pp. 12-15; Dincyurek, 2002, p. 26).

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“Spatial concept” which was one of the most significant subjects among scholars such as Bruskill, Leroy and Presciozi is going to be used in this research. Mentioned approach mainly emphasizing the organization and articulation of spaces and volume in different scale.

Due to Cuisenier, spatial approaches to vernacular architecture were classified in three tasks. First, there is the ethnographical and phenomenological tasks, that could be, perceive from the daily life of inhabitant of the specific region. Second is the sociological and ethological task, which is more based on the interaction of inhabitant’s social life, such as; economy, language, religion and beliefs and etc. Final tasks were termed as architectural and anthropological, which is representing the interpretation of the types and style of buildings, constructors and users (Cuisenier, 1997, p. 60).

From another point of view spatial approach to vernacular architecture could be categorize and achieve in two extensive methods. The first one was observation of building and examination of inhabitant interaction in building construction and usage. Second methodology was based on living experience of built spaces and from that to obtained and perceived how the buildings were considered and construct. Also, it should be mentioned that in followings research, both methodology would be use (Cuisenier, 1997, p. 60).

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Instead, majority of the designer, who are interested in geographic studies, attempt to emphasize the climate impacts as the principal excuses of establishing the rural contexts. Several scholars claimed that, the local materials, and in parallel, some other ones remark defensive reasons are the general formation of the settlements. Also others point out the formation of rural settlements is deeply affected by economical indicators. It has to be stated that the religious and cultural values are importantly taking role, for which researchers can concentrate on (Ghobadian, 2009; Reza, 2011).

Furthermore, as Zargar (1999) states; none of these factors (geography, economy, culture, community) can work independently and they have strong correlation in between each other (Zargar, 1999; Reza, 2011) (Fig 1).

Figure 1: Effective Factors in Shaping Villages (Zargar, 1999, p: 30)

As Oliver motioned, “Only by identification and labelling can classes and categories be identified that make reference possible to unseen or recollected phenomena.

Village Framework

Community Geography

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Effective parameter that shaping the pattern of the villages is going to be investigates from macro to micro scale. First scale, is defined the establishment scale and it is highlighting the location of the villages. Second scale is mainly investigating on spatial organization of the villages, where through the placement of built environment, fields and farms, rout and roads, bridges and etc.

Third scale is specifically, focusing on the built environment of the villages by examination of the passages, density, plot sizes, shape and organization of plots, the place of social activities, chamber, and etc.

Fourth scale, is relating with analysis of the building units accordingly to shape and internal organization of the houses, quality of spaces, composition of spaces and etc.

Final range, are reflecting the micro scale analysis of building components and construction details such as doors, windows, roof, faced and etc. It should be mentioned in all scales of mentioned investigation, the impact of external effect should be considered.

Geography is a significant aspect, which is commanding the shape of vernacular villages. Mentioned terminology will be categorized in two disciplines, which called as artificial and natural geography. This categorization is clarifying the geographical interpretation.

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natural geography mainly, identifying with environmental factors such as; water, wind, rain, snow, temperature, humidity, sun saturation, topography and etc.

The overview indicates that there is a strong relationship between the geographical aspects and formation of vernacular settlements that is going to be specifically examined in the following part of this dissertation.

More specifically, as Dincyurek mentioned; “For understanding the vernacular architecture in the world, divers classifications can be used. Geography, cultural landscape, population density, and climate are the major determinants of the classifications in the world in order to identify the place within the context. Among the mentioned classifications, the climatic classification is the most striking approach to understand the divergences and penetrations of the vernacular architecture in the world” (Dincyurek, 2002, p. 40).

Also, Oliver emphasize that; “Climate is the most determine environmental factor in the development of human –life” (Oliver, 1997).

In addition, “Climate is integration in time of the physical state of the atmospheric environmental characteristic of a certain geographical location” (Shaterian, 2011).

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Jeffrey Cook, in the vernacular architecture of the world encyclopaedia, categorized the climatic zones of the world, in nine distinctive regions as; Arctic and sub-Arctic, Continental, Desert, Maritime, Mediterranean, Monsoon, Montane, Subtropical, Tropical (Cook, 1997).

2.3 Identification of Iranian Vernacular Architecture in Terms of

Geographical Values

Iran is a mountainous country. In view of the fact that there are many variations in the general topography of the mountainous regions of the country in respect of both the climate and the geography much, can be explored in precedents of vernacular architecture. For this reason, this research is aimed to indicate and analyze the Iranian vernacular architecture (Reza, 2011). The characteristics of Iranian vernacular architecture will be argued by regarding to the geographical, topographical and climatic factors.

2.3.1 Geographical Value of Iranian Vernacular Architecture

Iran as a vast country, placed in the Middle East is occupied 1,648,000 km2 of square area. The country shares its boundaries by neighbouring countries including Turkmenistan, Azerbaijan and Armenia in the north side. Also, Afghanistan and Pakistan are lying to the east boundary of country and Turkey and Iraq to the West one.

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and the West by considering to the spiritual, cultural and political factors (Shaterian, 2011).

2.3.2 Location and Topographical Factors in Iranian Vernacular Architecture The topographical aspects are classified with regards to the physical appearance of the regions. In the consequence, Oliver, categorized the topography as, below-ground, coastal, desertic, and forest, grassland, lacustrine, lowland, marine, riparian, slope, upland and valley. Moreover, the inhabited zones are classified distinguishably, according to their organizations including; cluster, compact, compound, dispread, grid, linear, nodal, organic and peripheral are the different type of villages’ organization (Oliver, 1997). Subsequently this research is focus on the linear typology of rural settlements.

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1. 2.

3. 4.

Figure 2: Map of Iran with the Location of Villages (left), Kandovan (1), Masouleh (2), Abyaneh (3), Maymand (4) [1][2][3][4]

Iranians vernacular architecture has altered classification, due to the geographical, cultural and climatic factors. In respect to this, the research is focused on Iranian rural settlements with extroverted orientation, which are located in the zones that have steep topographical characteristics.

Therefore, the focus will be on the villages of Masouleh and Abyaneh, which have a similar steep topography. Then, the climatic factors on the one hand and the topographical issues on the other hand, will be the distinctive variables. Masouleh, as the first villages, is located in the northern part of Iran. This village is 1,050 meters above sea level in the Alborz mountain range, near the southern coast of the Caspian Sea.

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Figure 3: Map of Iran, Location of Masouleh and Abyaneh [5]

“Moreover, half of Iran is mountainous area and the other half is semi-desert and fertile agriculture planes prone. The general mountains of Iran consist of two huge arches, which stretched out from Azerbaijan to Afghanistan and encompass all the southern part of Caspian Sea. The other arches starting from Azerbaijan and continues to the west and south. These two arches surrounded the tree side of Iran (South, East and West) and not allow atmospheric phenomenon gets inside to Iran and the only open side is eastern side which has access to the Turkestan plains and central Asia” (Reza, 2011).

To sum up, this research is focused on the vernacular architecture with projected form from the terrains, in steep topography.

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also act as pathways in both villages. This approach creates a distinct elevation of differing angles for these villages. Masouleh’s settlements are positioned at a 47-degree angle approximately and those of Abyaneh at around a 29-47-degree angle (Figure 4). As a result, Masouleh housing developments are denser in comparison to the housing developments in Abyaneh. Therefore, the combination and integration of public and private space, in respect of the use of the roofs as pedestrian paths is more visible in the case of Masouleh village.

Figure 4: Section and Angle of Masouleh Village (left) and Abyaneh Village (right), (by author)

In both villages, the interconnection amongst the mountains, the village and the river creates an integrated unity between the nature and the built environment. In accordance with this, agricultural fields are located to the west and east orientation of the valley and orchards are located in south side of these villages.

2.3.3 Climatic Factors in Iranian Vernacular Architecture

With reference to the construction of vernacular houses, climatic conditions are of primary concern worldwide. Throughout the generations, human beings have designed and constructed their dwellings according to the climatic conditions, aiming to meet the most convenient life style (Reza & Dincyurek, 2017).

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include six winters and five summers. By using Olgyay’s method, Riazee has done his research by regarding to perspectives based on the building construction and human comfort conditions. In parallel with, Ganji generally recommended four divided climates zone in Iran, which are temperate and humid climate (southern side of Caspian Sea), cool climate (Western Mountain), hot and dry climate (central plateau), hot and humid climate- northern shores of Persian Gulf (Reza, 2011).

The climatic zoning of this study is based on the findings of Ghobadian (Ghobadian, 2009). As he stated, Iran is generalized in the category of dry countries. In fact, by considering its climatic diversity, it can be introduced into four main climatic regions:

• The Northern Coastal Region Temperate climate. • The Central Plateau Region Hot and Dry Climate.

• The Mountainous and High Plateau Region-Cold Climate.

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By regarding to Ghobadian’s classification, the selected case studies are located in first, second and third region, therefore the climate characteristics of fourth region is not going to be explaining in this study (Reza & Dincyurek, 2017).

Therefore, these diverse climatic conditions affect the construction style of the houses in each climatic region. In the temperate climate of region one, houses have been faced to the outside with the help of locating the opening on the external walls aimed to increase cross ventilation amongst the hot seasons of the year in the central plateau region, which dominantly have various hot and dry climate during summer and cold in winter.

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By considering the cold climate conditions in the villages standing on mountainous regions, the buildings’ openings are mostly faced to the south aiming to absorb natural light. Also, other three exterior walls of the house are adjacent to the soil and the neighbour house for avoiding the heat loss. The dwelling typologies for this specific climate zone are given below (Figure 6).

Figure 6: Climatic Map of Iran and Building Typologies (by author)

2.4 Terraced Housing Formation in Vernacular Iranian Settlements:

Masouleh and Abyaneh Villages

Available natural resources has shaped the settlements, and as water is an essential requirement for life, villages are established close to water sources such as rivers, aqua ducts, oases and springs.

1.The Northern Coastal The Northern Coastal Region (Temperate Climate)

2.The Central Plateau Region (Hot and Dry Climate)

3.The Mountainous and High Plateau Region (Cold Climate)

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Moreover, Abyaneh Village is feed for water by “Do Abi” spring, which flows constantly during a year (Memarian, 1997).

The abounded old pattern of Masouleh -old Masouleh or Kohneh Masouleh in local dialect-, was founded roughly 1006 AD, which located nowadays below in the new pattern towards the northwest. The inhabitant has been replaced from the old pattern of Masouleh to the current one, due to the possible attacks from neighboring villages and the risk of infectious diseases.

Various thoughts indicate on the history of Abyaneh village by referring to the civilization of Sialk (archaeological site near Kashan) is declared with 6,000 years old. It is supposed that Abyaneh village could have been emerged from one of those communities. This village has a square area of approximately 70,000 metres (Ghorbanizadeh & Abyaneh, 2008).

2.4.1 Topography of Masouleh and Abyaneh Villages

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Therefore, the combination and integration of public and private space, in respect of the use of the roofs as pedestrian paths is more visible in the case of Masouleh village.

In both villages the interconnection between the mountains, the village and the river creates an integrated unity between nature and the built environment. In accordance with, agricultural fields are arranged to the outer east and west sides of the rural settlements and in addition, orchards are situated in the southern position.

There are two concerning facts which should be consider in respect to developments on the skirts of mountain ranges. The first natural disaster is the de facto avalanches. As a result of their experience the local people have not carried out any construction work on avalanche routes. Secondly, if construction work did take place on the hillside for some special reason, the villagers were always careful about the possibility of falling rocks and avalanches and took some safety precautions. For example, in order to afford themselves some protection against possible avalanches and falling rubble, they harvest and forage the plans, which grow on the slopes because of the presence of this flora increases the temperature of the soil and as a result of the increased temperature the snow masses tend to lateral movement and to create avalanches.

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the movement of these rocks destroyed many houses and caused many fatalities (Zargar, 1999).

In addition, Ghaleeh Kooh mountain skirts serve as the settlement location of Abyaneh village. The village rounds parallel to the valley and perpendicular to the main route between Kashan city and Natanz (Figure 7).

Figure 7: Location of Masouleh (left) and Abyaneh (right) Villages (by author)

As mentioned, both of these villages have high dens housing morphology caused by the natural environmental factors. Hence, dwellings are situated in the rectangular-shaped steep slope, and parallel with the main pathway of the village.

2.4.2 Climatic Factors of Masouleh and Abyaneh Villages

There is a strong integration in between Masouleh and Abyaneh villages and gentle sloping surroundings, which has a constrained space and interconnection between mountain, villages and stream constrained nearby individuals to move their agribusiness fields, a long way from their settlements.

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climate, and the mountainous and high plateau region, which has a cold climate. Therefore, these villages have a multi climatic character (Figure 8).

Figure 8: Location of Masouleh and Abyaneh on the Border of Different Climatic Regions (by author)

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However, this outward-oriented design of buildings is also present in Iran’s western mountains and the central plateau where it is not so humid as e.g. with Abyaneh village.

2.4.3 Urban Patterns and Spatial Relations of Masouleh and Abyaneh Villages In Masouleh and Abyaneh villages, dwellings have been built standing on ground level, which give opportunity to be opened on two to four orientations. Balconies act as type of space to transit in between the built and the natural environment, thus mentioned transitional spaces integrate internal and external spaces in the settlements. Therefore, local residents also installed large windows on the main elevation. According to Memarian, the urban context of these villages, has created a kind of symbiosis between that of the green space of the natural environment and the architecture as a built environment, this example, therefore, demonstrate the representation of essential principles of the ‘nature friendly design’ terminology (Memarian, 1997).

As the aftereffect of these findings account of morphology, this village portrays exceptionally unmistakable components, which are welcoming people, and it bears a run of the mill character in context.

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Chapter 3 THOROUGH INVESTIGATIONS OF FRACTAL AND

CELLULAR AUTOMATA THEORIES

3.1 Chaos Theory, Complexity and Emergence Concepts

Complexity Science is a methodology, which presents elective models rather than conventional investigative techniques as an efficient and fathomable structure for complex frameworks. Newtonian physics details the deliberate structure obviously; along these lines setting up its utilization in all examination regions of science, building, connected science, business administration, etc.(Reza & Dincyurek, 2015).

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Figure 10: Four Jumps to Consciousness (Jenks, 1997)

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“During the 20th century the revolution of non-linear and quantum physics and the theories of relativity, based on a time and space assumption, resulted in the emergence of the chaos theory, which opening up non-linear systems. When scoping onto the global environment, it is clear that natural phenomenon are highly interconnected, interdependent and non-linear and, therefore, can be referred to as complex systems, thus shaping and defining the border between traditional and modern science. Traditional science attempts to eliminate complexities by studying the individual components of a system within an isolated environment” (Reza & Dincyurek, 2015).

Being a standout amongst the most imperative attributes of non-linear frameworks, self-similarities frameworks saw its advancement from regular and organic frameworks before it broadened into the distinctive fields of software engineering, economy and etc.; (Complexity Learning Lab, n.d.). Nevertheless, before proceeding to the explanation of the self-organization characteristics, the concept of “system” is defined as follows:

According to the Oxford Dictionary, “a system is a set of things working together as parts of a mechanism; a complex whole.” Therefore the result could be the part of mechanism or an interconnecting network.

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other's conduct. This adjusts to the second Newtonian law which expresses that every action has an opposite and equal reaction (Reza & Dincyurek, 2015).

Accordingly, this study will predominantly concentrate on the conduct of complex system when connected in design and architecture. The key thought behind the complexity hypothesis is that after various iterations utilizing small, basic parts, which are duplicated, consolidated or changed, through basic standards, a differing framework, whose future state is not effortlessly unsurprising, emerges. The new data, which the framework gives back, gives chances to an analogical extrapolation specifically from different procedures in design, which results in a spatial form and configuration pattern. This is exceptionally useful to planners as they consistently take a gander at living life forms that get their mind boggling shapes and behavioural examples, through their communications in space, here and there over drawn out stretches of time (Reza & Dincyurek, 2015).

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complex forms and behavioral patterns, through their interactions in space, sometimes over long periods of time (Reza & Dincyurek, 2015, p. 62).

In the province of architecture, complexity is not only a mathematical thought procured from science and the characteristic world, which is then connected in outline. It is a natural quality in the realm of construction development, clear in the example of development and advancements of settlements. Just the patterns characterize as old, while the mathematical methodology then again is later. It is required to notice that in city making, the cosmological, hierarchical and geometrical movement in context permits the engagement with the city, starting from the earliest stage because of the discrete granular strengths, which it unfurls. Then again, since the nineteenth century, and even at times, the pioneer arranging urban plans areas from top-down (Reza & Dincyurek, 2015, p. 63).

As Batty & Longley (1994) observed, “The concern for more micro issues, for thinking of cities in terms of the actions of individuals, came from another area entirely: ideas about disaggregation and heterogeneity. Batty uses these ideas in city simulation, studying emergence through cells” (Batty & Longley, 1994).

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in the multifarious modern city. Such an approach has both analytical and generative potential. What does a similar focus and process means, in terms of aesthetics, materiality and responsiveness, at the scale of the individual architectural project” (Burry & Burry , 2010, p. 53).

On the other hand as Jencks (1997) claimed; “As we have seen the inadequacy of Modern architecture, and the necessity for creating an architecture of organizational depth, but that still leaves important questions open. Is there one language of architecture, which is more suited to the contemporary situation than another? Is there an answer to the perennial question - asked since the early nineteenth century - 'in which style shall we build?' Before taking on this recurrent query I will examine several of the emergent languages, which are inspired by, or revealing of, Complexity and Chaos theories. Therefore, I will touch on nine or so identifiable departures of the last several years, starting with the analogies, which have become so familiar with the emergence of Chaos Theory” (Jencks, 1997).

3.2 Definitions and History of Fractal Concept

Before explaining the fractal theory, it is important to understand the root of the word fractal. The term fractal comes from the Latin word ‘fractus,’ which means ‘broken’ or ‘irregular’ or ‘unsmooth’(Reza & Dincyurek, 2015).

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many definitions for the fractal dimensions of a fractal set” (Tang, Tao, & Lam, 2002).

As Bovill (1996) mentioned: “There is symmetry in nature, but on closer observation there is also a complex diversity. Not all humans are the same size and shape. This was the self-similarity, which can be perceived from nature from macro scale. As he mentioned: oak trees are not identical. There is however, a newly developed concept to size. It has self-similarity, in which small parts of an object are similar to larger parts of the object”. This self-similarity can be seen in Figure 12 as the formation of the Sierpinski gasket (McGuire, 1990).

Additionally, Mandelbrot (1989): Comprehensively, mathematical and natural fractals are shapes whose roughness and fragmentation neither have a tendency to vanish or vacillate here and there, yet remain basically unaltered as one zooms in and examination is refined. Subsequently the structure of each piece holds the way to the entire structure.

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As Jacob (2008) pointed out in his dissertation; “Randomness can be introduced into this formation. In ‘An Eye for Fractals’, Michael McGuire illustrates this by randomly picking a point on sides of the triangle instead of the mid-point as observed above. After only eight iterations, a mountainside with rugged rock outcrops can be observed” (Figure 13).

Figure 13: Introducing Randomness (McGuire, 1990)

Also, as Bovill (1996); referred to Michael Barnsley, in his book ‘Fractal Everywhere’, provides this warning in his introduction:

“Fractal Geometry will make you see everything differently. There is a danger in reading further. You risk the loss of your childhood vision of clouds, forests, galaxies, leaves, feathers, flowers, rocks, mountains, torrents of water, carpet, bricks, and much else besides. Never again will your interpretation of these things be quite the same.”

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randomness and self-similarity of a vernacular settlement, which is going to be discussed in following chapters.

3.2.1 Fractal Theory

According to Burry & Burry (2010), in ‘The new mathematics of architecture’: “Intuitive meaning. That has a form, either exceedingly irregular, or exceedingly fractured or fragmented, and continues to be so whatever the scale it is examined at. That contains distinguishing elements whose scales are highly varied and cover a very broad range” (Burry & Burry , 2010).

Apart from mentioned spontaneous meaning of fractal, configuration of fractal set or object should be clarified. “The word fractal does not distinguish, intentionally, between mathematical sets (theory) and natural objects (reality): it is used in those cases in which its generality and the resulting intentional ambiguity are either desired, made clear by the context, or do not entail associated drawbacks” (Burry & Burry , 2010).

Between uncontrolled chaos absolute disorder and Euclidean order, for characterizing the "segment of fractal order", the mathematician Benoit Mandelbrot, characterized the clarification of the topographical structure's relief in the mid-sixties by some basic inquiry:

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natural process to abstract numerical simulations obtained using computational techniques” (Mandelbrot & Frame, 2003).

In fact, “Fractal geometry has had a revolutionary impact upon the theories of physics, especially in the construction of mathematical model of phenomena that appeared to be governed by a casual or unpredictable order. Not only turbulence phenomena (as in the expansion of a gas in the air), but also natural patterns have been characterized by irregularity (the profile of a shoreline, the shape of the tree, land reliefs, etc.) and dynamical structures of temporal-spatial development (clusters, multitudes, deployments, etc.) The characteristics of fractal permit, in effect, a definition of elastic pattern of evolutionary topologies that characterize such phenomena. Also, fractal objects do not have a dimension that is measurable by a whole number. Their dimensionality is found precisely along the boundary between lines, planes and volumes. They are more efficient at occupying space than their real counterparts. They are more dense than lines, but without arriving at massifying on plane, like a spongy ball of yarn” (Burry & Burry , 2010, p. 474).

Beside this, one of the results of the vast point of interest of a fractal object is that, they basically don’t have any conclusive absolute size, and such scalar uncertainty presents globalist in locality and, most importantly, allows ‘local’ transferences of the part to the entire: what is called ‘scalar jump’ (Jencks, 1997).

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clearly constructed by very simple elements. The new digital geometry and the expansion of CAD enable us, more than ever, to interpret such developments. If fractal geometry is the way to joining form and function, the coming decade should see the emergence of a new theory that demonstrates how form and function coevolve spontaneously through new dynamic design” (Batty & Longley, 1994). 3.2.2 Comparison of Euclidean Geometry and Fractal Geometry

In order to clarify the essence of fractal geometry, this study will use the comparison of Euclidean Geometry with fractal geometry, by referring to different characteristics, which was presented by Jacob (2008) in Table 1 given below.

As it is mentioned in previous studies; the fundamental assumption behind fractal geometry was specifically influenced by the planners and decision makers and opened new skylines for them in the field of contemporary art and architecture approaches. As aforementioned stated, fractal geometry depends on scientific calculations and non-direct material science. Truly, it's mandatory to locate a special ratio, which is known as the fractal dimension. In the accompanying segment, this study will concentrate on depicting the significance of the fractal measurement. Besides, the most valuable strategy for finding the fractal measurement will likewise be clarified (Reza & Dincyurek, 2015, p. 64).

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parts of the object and its overall characteristics process rather than equations. This process which represent the object is viewed from different distances, with the same degree of detail and analyses and represent things in the course of time.” (Burry & Burry , 2010)

On the other hand, by explaining the characteristic of Euclidean geometry, and by defining the differentiation of mentioned geometry with fractal geometry, the necessity of fractal geometries will be clear more.

“Euclidean shapes do not display a cascade of textural depth. On closer observation, Euclidean shapes remain straight lines and smooth curves. The Koch curve is an example of a fractal. It is created in a recursive way, mapping itself at smaller and smaller scales. It displays a cascade of self-similar structure.” (Bovill, 1996)

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Table 1: The comparison of Euclidean geometry with fractal geometry (Haggard, Cooper, & Gyovai, 2006; Jacob, 2008, p. 15; Reza & Dincyurek, 2015, p. 65)

ABOUT Basic assumptions behind Euclidean geometry (200 years old) Basic assumptions behind fractal geometry (20 years old) 1. Description The main concern is the

description of –man-made objects. Natural objects are assumed to be difficult to describe or are indescribable in geometric terms.

There is holistic reality, infinitely complex but geometrically describe- able which we call nature.

2. Form Simple rules give simple forms. Complex forms require complex rules; therefore simplicity is a virtue.

Infinitely complex forms are easy to generate by simple means. Complexity is an accessible to us. Simplicity can be a virtue, but can also be simplistic. Complexity is our biological heritage.

3. Form generation Formulae are the generator of form.

Iteration and feedback is the generator of form.

4. Randomness Randomness has no place in geometry.

Randomness can be part of the form generating process.

5. Dimension There are three whole numbered dimensions.

There are an infinite number of dimensions that can fill the gaps between one, two and three dimensions

6. Infinity Infinity is not dealt with in geometry

Infinity is an everyday quality and part of geometry.

7. Length Length is fixed and measurable

Length is often infinite.

8. Scale Scale is the relative size of objects to ourselves, other objects, or

systems ofmeasurement

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9. Order Order is predictable and desirable. Disorder is unpredictable and undesirable

Order can be very complex; order and perceived disorder are not discrete things but often aspects of the same thing.

10. Reality Reality is dualistic with order and disorder in opposition to each other.

Reality is complex, diverse and holistic. Duality between order and disorder is

sometimes a useful tool, often an illusion and sometimes a delusion.

11. Harmony Harmony can be achieved by simplification.

Harmony can be achieved by complexity.

12. Order & dynamics Control is an essential part of aesthetics.

Dancing with chaos is an essential part of aesthetics.

13. Symmetry Symmetry and asymmetry are important aesthetic devices.

Self –Similarity and affined similarity are also important aesthetic devices.

14. Form expression Geometrical solids are the basic building blocks of aesthetics because they deal with differentiation.

Fluidity is an essential part of aesthetics because it deals with connectivity and process.

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According to this definition Bovill mentioned; “ Mandelbort’s fractal geometry has the capacity of describing the cascade of detail observed in these natural forms. The relationship between nature fractal geometry is often introduced through the example of the length of a coastline. As the length of the instrument one uses to measure a coastline gets smaller, the measured length of the coastline gets longer as smaller and smaller bays and inlets are included in the measurement. A natural rocky coastline displays a progression of detail similar to the Koch curve, except that it’s meandering is random. Moreover, “Architecture composition is concerned with the progression of interesting forms from the distant view of the elevation to the intimate details. This progression is necessary to maintain interest. As one approach and enters a building, there should always be another smaller-scale, interesting detail that express the overall intent of the composition. This is a fractal concept. Fractal Geometry is the formal study of this progression of self-similarities detail from large to small scale” (Bovill, 1996).

3.2.3 Definition of Fractal Dimension

The Elucidation of Terraced Housing in Iranian Vernacular Architecture through Fractal Models: In Case of Masouleh and Abyaneh Settlements